Given a prime number p, Bloch and Kato showed how the p8-Selmer group of an abelian variety A over a number field K is determined by the p-adic Tate module. In general, the p-Selmer group Selpm A need not be determined by the mod p Galois representation Arps; we show, however, that this is the case if p is large enough. More precisely, we exhibit a finite explicit set of rational primes Σ depen...